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A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems

2017; Wiley; Volume: 24; Issue: 1-2 Linguagem: Inglês

10.1002/mcda.1604

1099-1360

Rodrigo Lankaites Pinheiro, Dario Landa-Silva, Jason Atkin,

Optimization and Mathematical Programming

Journal of Multi-Criteria Decision AnalysisVolume 24, Issue 1-2 p. 37-56 RESEARCH ARTICLE A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems Rodrigo Lankaites Pinheiro, Corresponding Author Rodrigo Lankaites Pinheiro rlpinheiro@ymail.com Asap Research Group, School of Computer Science, the University of Nottingham, Nottingham, UK Correspondence Rodrigo Lankaites Pinheiro, Asap Research Group, School of Computer Science, the University of Nottingham, Nottingham, UK. Email: rlpinheiro@ymail.comSearch for more papers by this authorDario Landa-Silva, Dario Landa-Silva Asap Research Group, School of Computer Science, the University of Nottingham, Nottingham, UKSearch for more papers by this authorJason Atkin, Jason Atkin Asap Research Group, School of Computer Science, the University of Nottingham, Nottingham, UKSearch for more papers by this author Rodrigo Lankaites Pinheiro, Corresponding Author Rodrigo Lankaites Pinheiro rlpinheiro@ymail.com Asap Research Group, School of Computer Science, the University of Nottingham, Nottingham, UK Correspondence Rodrigo Lankaites Pinheiro, Asap Research Group, School of Computer Science, the University of Nottingham, Nottingham, UK. Email: rlpinheiro@ymail.comSearch for more papers by this authorDario Landa-Silva, Dario Landa-Silva Asap Research Group, School of Computer Science, the University of Nottingham, Nottingham, UKSearch for more papers by this authorJason Atkin, Jason Atkin Asap Research Group, School of Computer Science, the University of Nottingham, Nottingham, UKSearch for more papers by this author First published: 06 March 2017 https://doi.org/10.1002/mcda.1604Citations: 4Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives, that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: First, the global pairwise relationships are analysed using the Kendall correlation method; then, the ranges of the values found on the given Pareto front are estimated and assessed; next, these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally, local relationships are identified using scatter plots. Experiments are presented for three combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem, and multiobjective vehicle routing problem with time windows . Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives. Citing Literature Volume24, Issue1-2January-April 2017Pages 37-56 RelatedInformation